Abstract: Let , , be a strongly continuous submarkovian semigroup on a real Hilbert space . The measure m is assumed to be excessive and the generator A is assumed to satisfy an estimate (the sector condition) which permits the application of Dirichlet spaces (not necessarily symmetric). Other submarkovian semigroups with the same local generator and cogenerator and relative to which m is again excessive are classified in terms of generators for processes which live on a suitable boundary.